Abstract
AbstractOne investigates the post-shut-in growth of a plane-strain hydraulic fracture in an impermeable medium while accounting for the possible presence of a fluid lag. After the stop of fluid injection, the fracture may present three distinct propagation patterns: an immediate arrest, a temporary arrest with delayed propagation, and a continuous fracture growth. These three patterns are all followed by a final fracture arrest yet the fracture behaviour prior to that results from the interplay between the dimensionless toughness $$\mathcal {K}_m$$
K
m
, the shut-in time $$t_s/t_{om}$$
t
s
/
t
om
, and the propagation time $$t/t_s$$
t
/
t
s
. $$\mathcal {K}_m$$
K
m
characterizes the energy dissipation ratio between fracture surface creation and viscous fluid flow under constant rate injection. $$t_s$$
t
s
and $$t_{om}$$
t
om
represent respectively the timescale of shut-in and the coalescence of the fluid and fracture fronts. The immediate arrest occurs when the fracture toughness dominates the fracture growth at the stop of injection ($$\mathcal {K}_m \gtrapprox 4.3$$
K
m
⪆
4.3
). It may also occur upon an early shut-in at low dimensionless toughness associated with an overshoot of fracture extension and a significant fluid lag. For intermediate values of $$\mathcal {K}_m$$
K
m
and $$t_s/t_{om}$$
t
s
/
t
om
, the fracture may experience a temporary arrest followed by a restart of fracture propagation. The period of the temporary arrest becomes shorter with higher dimensionless toughness and later shut-in until it drops to zero. The fracture behaviour after shut-in then transitions from temporary arrest to continuous propagation. These propagation patterns result in different evolution of fracture dimensions which possibly explains the various emplacement scaling relations reported in magmatic dikes.
Publisher
Springer Science and Business Media LLC
Subject
Geology,Geotechnical Engineering and Engineering Geology,Civil and Structural Engineering